Which Alice?

ALICE IN PUZZLE-LAND
ten tarts. Now, all the nonfavorites have had all the tarts they are
going to get, whereas each favorite is to get one more tart. So the
ten remaining tarts are all for the favorites—one to each favorite. So
there must be ten favorites.
Let us check: The ten favorites each get four tarts, which makes
forty tarts. The other twenty guests each get three tarts apiece,
which makes sixty tarts. Since forty plus sixty equals one hundred,
we see our solution is correct.
LARGE TARTS AND SMALL TARTS Since each large tart is
worth three small ones, then seven large tarts are worth twenty-one
small ones, so seven large ones and four small ones are worth
twenty-five small ones. On the other hand, four large ones and
seven small ones are worth the same as nineteen small ones (because
four large ones are worth twelve small ones). So the difference in
price between twenty-five small ones and nineteen small ones is
twelve cents. This means that six tarts (six is twenty-five minus
nineteen) are worth twelve cents, so each small tart is worth two
cents and each large tart is worth six cents.
Let us check: Four large tarts and seven small ones would cost 24
+ 14 = 38 cents, whereas seven large tarts and four small ones
would cost 42 + 8 = 50 cents, which is indeed 12 cents more than
38 cents.
THE VISIT The Cheshire Cat must have found two tarts,
eaten half of them plus one, leaving none. The Dormouse must
have found six tarts, eaten half of them plus one, leaving two for
the Cheshire Cat. The March Hare found fourteen, ate seven plus
one, leaving six. The Hatter found thirty, ate fifteen plus one,
leaving fourteen. So there were thirty tarts to begin with.
HOW MANY DAYS DID HE WORK? The maximum number
of tarts the gardener can earn is 78 (3 x 26). He earned only 62
tarts,
152